Data Analysis and Linear Regression

The objective of statistics is to make inferences about a population based on information contained in a sample. Populations are characterized by parameters, such as mean, median, or standard deviation. A model will help us understand the exact relationship between different variables and how they are used to predict the outcome.

A look at one of the most commonly used statistical techniques in the world is regression. Regression analysis is the modeling of the relationship between a response variable and a set of explanatory variables. It is one of the more widely used all statistical techniques.

A regression model provides the user with a functional relationship between the target variable and explanatory variables that allows the user to determine which of the predictors variables have an effect on the response. The regression model allows the user to explore what happens to the target variable for specified changes in the predictors' variables.

An example of this could be to find the relationship between an employee's efficiency on a company as a target variable and explanatory variables such as experience on similar jobs, educational background, and previous training.

The basic idea of regression analysis is to obtain a model for the functional relationship between the response (target) variable (sometimes called dependent variable) and one or more explanatory (predictor) variables (sometimes called independent variables).

Some characteristics of regression models are:

The most simple form of a regression model is Simple Linear Regression. Simple linear regression is a method that helps to understand the relationship between two variables:

The result of the linear regression is a linear function that predicts the response variable (dependent) based on the predictor variable (independent).

Basically, it’s the equation of a straight line. The constant term is called the intercept of the linear regression and is interpreted as the predicted value of y when x = 0. The coefficient of the x is the slope of the line. In other words, the predicted change in y is when there is a one-unit change in x.

The slope quantifies the relationship between the predictor and the outcome. Relationships can be positive or negative. If the slope coefficient of a model is positive, it describes a positive relationship, whereas a line with a negative slope describes a negative relationship.

Simple linear regression is a straightforward method for fitting a prediction line between a single dependent variable y and a single independent variable x. In simple regression, the basic assumption is that the relationship is linear.

There is a term called assumption of linearity, which tells that the slope of the equation does not change as x changes.

In Python, you can use the Linear Regression model by importing it from the scikit-learn model.

To use the linear regression model, we need to create an object, as follows:

You can use a column from a data frame as a predictor variable (X) and another column as a response variable (Y). In order to use the model, we use the fit method.

And then you can make a prediction:

You can also find the value of the intercept value with:

And the value of the slope (or gradient) with:

With those values, you can find the equation of the model.

This was an introduction to a simple linear regression model and how does it work. Also, we can use the linear model with several predictions which can give us a more complex (not really) equation. There exists also Polynomial regressions but that will be the subject of another article.

This was a topic from a notebook of the IBM course on Data Analysis with Python. You can check the next link to view some of the topics and notebooks of that course (in Spanish).

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